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Type of mathematical function
In mathematics, a locally constant function is a function from a topological space into a set with the property that around every point of its domain
Locally_constant_function
Strong form of uniform continuity
called the Lipschitz constant of the function (and is related to the modulus of uniform continuity). For instance, every function that is defined on an
Lipschitz_continuity
Type of mathematical function
In mathematics, a constant function is a function whose (output) value is the same for every input value. As a real-valued function of a real-valued argument
Constant_function
Topological space
subspace of the space of continuous functions is the locally constant functions. A function is locally constant if there is a partition of the Cantor
Cantor_space
Linear combination of indicator functions of real intervals
still be locally finite, resulting in the definition of piecewise constant functions. A constant function is a trivial example of a step function. Then there
Step_function
Function which is integrable on its domain
In mathematics, a locally integrable function (sometimes also called locally summable function) is a function which is integrable (so its integral is
Locally_integrable_function
the Dirichlet function. Locally constant function: a continuous function into a discrete space. Homeomorphism: is a bijective function that is also continuous
List_of_types_of_functions
a bounded function, for which the constant does not depend on x . {\displaystyle x.} Obviously, if a function is bounded then it is locally bounded. The
Local_boundedness
Direct summand of a free module (mathematics)
is a locally constant function on X. In particular, if X is connected (that is if R has no other idempotents than 0 and 1), then P has constant rank.
Projective_module
Sheaf theory
In algebraic topology, a locally constant sheaf on a topological space X is a sheaf F {\displaystyle {\mathcal {F}}} on X such that for each x in X, there
Locally_constant_sheaf
Constant expressing ambiguity from indefinite integrals
constant of integration, often denoted by C {\displaystyle C} (or c {\displaystyle c} ), is a constant term added to an antiderivative of a function f
Constant_of_integration
Type of continuity of a complex-valued function
> 1 {\displaystyle \alpha >1} is constant (see proof below). If α = 1 {\displaystyle \alpha =1} , then the function satisfies a Lipschitz condition. For
Hölder_condition
Class of mathematical function
can be expressed as the ratio between two holomorphic functions (with the denominator not constant 0) defined on D {\displaystyle D} : any pole must coincide
Meromorphic_function
Functions in mathematics
distributions. Each function above will yield another harmonic function when multiplied by a constant, rotated, and/or has a constant added. The inversion
Harmonic_function
mathematics, a Schwartz–Bruhat function, named after Laurent Schwartz and François Bruhat, is a complex valued function on a locally compact abelian group, such
Schwartz–Bruhat_function
Type of function in mathematics
an analytic function is a function that is locally represented by a convergent power series. More precisely, a real or complex function is analytic at
Analytic_function
Tool to track locally defined data attached to the open sets of a topological space
sheafification of the constant presheaf (see above) is called the constant sheaf. Despite its name, its sections are locally constant functions. The sheaf a F
Sheaf_(mathematics)
Object in mathematical sheaf theory
This sheaf may be identified with the sheaf of locally constant A {\displaystyle A} -valued functions on X {\displaystyle X} . In certain cases, the set
Constant_sheaf
Operation in Hamiltonian mechanics
the Lie bracket of vector fields, but this is true only up to a locally constant function. However, to prove the Jacobi identity for the Poisson bracket
Poisson_bracket
general form of the antiderivative replaces the constant of integration with a locally constant function. However, it is conventional to omit this from
List of integrals of rational functions
List_of_integrals_of_rational_functions
Complex-differentiable (mathematical) function
that a holomorphic function is infinitely differentiable and locally equal to its own Taylor series (is analytic). Holomorphic functions are the central
Holomorphic_function
Type of generating function in mathematics
{\displaystyle \phi :K^{n}\to \mathbb {C} } be a Schwartz–Bruhat function, i.e. a locally constant function with compact support and let χ {\displaystyle \chi } be
Igusa_zeta_function
( G ) {\displaystyle C_{c}^{\infty }(G)} denote the space of locally constant functions on G {\displaystyle G} with compact support. With the multiplicative
Locally_profinite_group
Inclusion of one mathematical structure in another, preserving properties of interest
locally injective if it is locally injective around every point of its domain. Similarly, a local (topological, resp. smooth) embedding is a function
Embedding
Order-preserving mathematical function
monotone need not be invertible; they may be constant on some interval (and therefore not one-to-one). A function may be strictly monotonic over a limited
Monotonic_function
On converting relations to functions of several real variables
equations is locally the graph of a function. Augustin-Louis Cauchy (1789–1857) is credited with the first rigorous form of the implicit function theorem.
Implicit_function_theorem
Tool in algebraic topology
group A {\displaystyle A} , the constant sheaf A X {\displaystyle A_{X}} means the sheaf of locally constant functions with values in A {\displaystyle
Sheaf_cohomology
function f, exp(f) is a non-vanishing holomorphic function, and exp(f + g) = exp(f)exp(g). Its kernel is the sheaf 2πiZ of locally constant functions
Exponential_sheaf_sequence
Concept in mathematics
geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials. It is also called a regular map.
Morphism of algebraic varieties
Morphism_of_algebraic_varieties
Theorem in mathematics
continuous but zero at a point, the function is no longer necessarily locally injective. A real function that is locally constant at a point x ∈ R {\displaystyle
Inverse_function_theorem
Concept of vector calculus
be called "exact". The cohomology classes are identified with locally constant functions. Using contracting homotopies similar to the one used in the proof
Closed and exact differential forms
Closed_and_exact_differential_forms
Space with topology generated by convex sets
functional analysis and related areas of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector
Locally convex topological vector space
Locally_convex_topological_vector_space
Number, approximately 3.14
τ {\displaystyle q=e^{\pi i\tau }} . The constant π is the unique constant making the Jacobi theta function an automorphic form, which means that it transforms
Pi
Type of mathematical object
is a locally free OS-module of finite rank. The rank is a locally constant function on S, and is called the order of G. The order of a constant group
Group_scheme
Branch of mathematics studying functions of a complex variable
is, at every point in its domain, locally given by a convergent power series. In essence, this means that functions holomorphic on Ω {\displaystyle \Omega
Complex_analysis
of G are (represented by) a finite locally free scheme. The group G(1) has rank ph for some locally constant function h on S, called the rank or height
Barsotti–Tate_group
Type of function in linear algebra
sublinear function (or functional as is more often used in functional analysis), also called a quasi-seminorm, on a vector space is a real-valued function with
Sublinear_function
Generalized function whose value is zero everywhere except at zero
analytic functions) by the Cauchy–Kovalevskaya theorem or (if the coefficients of L are constant) by quadrature. So, if the delta function can be decomposed
Dirac_delta_function
Tool in homological algebra
cohomology of this complex is called the de Rham cohomology of M. Locally constant functions are designated with its isomorphism ℜ c {\displaystyle \Re ^{c}}
Chain_complex
construction quotient Topological tensor product Discrete space Locally constant function Trivial topology Cofinite topology Cocountable topology Finer
List of general topology topics
List_of_general_topology_topics
Vector field defined for any energy function
algebra homomorphism, whose kernel consists of the locally constant functions (constant functions if M {\displaystyle M} is connected). See Lee (2003
Hamiltonian_vector_field
Mathematical transform that expresses a function of time as a function of frequency
{f}}(\xi ).} For example, the Fourier transform of the delta function is the constant function 1 {\displaystyle 1} : δ ( x ) ⟷ F 1. {\displaystyle
Fourier_transform
Duality for locally compact abelian groups
In mathematics, Pontryagin duality is a duality between locally compact abelian groups that allows generalizing Fourier transform to all such groups,
Pontryagin_duality
Property of topological spaces
instance, that a continuous function from a locally connected space to a totally disconnected space must be locally constant. In fact the openness of components
Locally_connected_space
Mathematical theorem in the study of analysis
which contains the constants and separates points. A version of the Stone–Weierstrass theorem is also true when X is only locally compact. Let C0(X, R)
Stone–Weierstrass_theorem
Function whose all derivatives vanish at a point
function is locally constant (that is, constant in at least one neighbourhood) of a point in the interior of its domain if and only if the function is
Flat_function
square numbers with constant second difference. Carmichael's totient function conjecture: do all values of Euler's totient function have multiplicity greater
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Objects that generalize functions
possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional
Distribution (mathematical analysis)
Distribution_(mathematical_analysis)
Mathematical theorem in complex analysis
{\displaystyle f} . In other words, either f {\displaystyle f} is locally a constant function, or, for any point z 0 {\displaystyle z_{0}} inside the domain
Maximum_modulus_principle
Mathematical operator in real and harmonic analysis
operator takes a locally integrable function f : R d → C {\displaystyle f:\mathbb {R} ^{d}\to \mathbb {C} } and returns another function M f : R d → [ 0
Hardy–Littlewood maximal function
Hardy–Littlewood_maximal_function
Observation in physical cosmology
coordinate. Though the Hubble constant H0 is constant at any given moment in time, the Hubble parameter H, of which the Hubble constant is the current value,
Hubble's_law
Specific algebraic group
dimension of the scheme) is called the rank of the torus, and it is a locally constant function on S. Most notions defined for tori over fields carry to this
Algebraic_torus
Type of mathematical expression
the function that it defines: a constant term and a constant polynomial define constant functions.[citation needed] In fact, as a homogeneous function, it
Polynomial
Logarithm of a complex number
negative real number. Like every holomorphic function, the complex logarithm can be represented locally – near any point in its domain – with a power
Complex_logarithm
locally free R-module of finite rank. This rank is called the degree of D and is denoted by deg D {\displaystyle \deg D} . It is a locally constant
Relative effective Cartier divisor
Relative_effective_Cartier_divisor
Study of mathematical algorithms for optimization problems
for minimization problems with convex functions and other locally Lipschitz functions, which meet in loss function minimization of the neural network. The
Mathematical_optimization
Type of mathematical function
Sawtooth function Floor function Step function, a function composed of constant sub-functions, so also called a piecewise constant function Boxcar function, Heaviside
Piecewise_linear_function
Expression that may be integrated over a region
|dx| on the interval is unambiguously 1 (i.e. the integral of the constant function 1 with respect to this measure is 1). Similarly, under a change of
Differential_form
Mathematical constant
locally close to equally spaced. They then derive a contradiction with known results on the local distribution of zeros of the Riemann zeta function,
De_Bruijn–Newman_constant
Smooth map which is a diffeomorphism upon restriction
also a local homeomorphism and therefore a locally injective open map. A local diffeomorphism has constant rank of n . {\displaystyle n.} A diffeomorphism
Local_diffeomorphism
Function spaces generalizing finite-dimensional p norm spaces
absolute deviations – Statistical optimality criterion Locally integrable function – Function which is integrable on its domain ( L loc 1 ) {\displaystyle
Lp_space
Mathematical parametrization of vector spaces by another space
trivializations show that the function x → k x {\displaystyle x\to k_{x}} is locally constant, and is therefore constant on each connected component of
Vector_bundle
Special function in the physical sciences
mathematics, the Airy function (or Airy function of the first kind) A i ( x ) {\displaystyle \mathbf {Ai({\boldsymbol {x}})} } is a special function named after
Airy_function
Concept in microeconomics
demand function isolates the effect of relative prices on demand, assuming utility remains constant. It contrasts with the Marshallian demand function, which
Hicksian_demand_function
Generalized mathematical function
as a multivalued function. The antiderivative of a function is the set of functions whose derivative is that function. The constant of integration follows
Multivalued_function
Moving average and polynomial regression method for smoothing data
developed for scatterplot smoothing, are LOESS (locally estimated scatterplot smoothing) and LOWESS (locally weighted scatterplot smoothing), both pronounced
Local_regression
Left-invariant (or right-invariant) measure on locally compact topological group
"invariant volume" to subsets of locally compact topological groups, consequently defining an integral for functions on those groups. This measure was
Haar_measure
Type of error-correcting code
-LTCs" namely locally testable codes with constant rate r {\displaystyle r} , constant distance δ {\displaystyle \delta } and constant locality q {\displaystyle
Locally_testable_code
Pattern defining an infinite sequence of numbers
{\displaystyle k} is two and the linear function merely adds the two previous terms. This example is a linear recurrence with constant coefficients, because the coefficients
Recurrence_relation
Fundamental trigonometric functions
{\displaystyle \Gamma } is the gamma function and ϖ {\displaystyle \varpi } is the lemniscate constant. The functions sin : R → R {\textstyle \sin :\mathbb
Sine_and_cosine
Concept in mathematics
real-valued functions on Ω {\displaystyle \Omega } . Moreover, the conjugate of u , {\displaystyle u,} if it exists, is unique up to an additive constant. Also
Harmonic_conjugate
Fourier transform of the probability density function
the characteristic function is its Fourier transform with sign reversal in the complex exponential. This convention for the constants appearing in the definition
Characteristic function (probability theory)
Characteristic_function_(probability_theory)
Sheaf of rings in mathematics
continuous (scalar-valued) functions on open subsets. Among ringed spaces, especially important and prominent is a locally ringed space: a ringed space
Ringed_space
Topological vector spaces
those that are induced locally integrable functions. The function f : U → R {\displaystyle f:U\to \mathbb {R} } is called locally integrable if it is Lebesgue
Spaces of test functions and distributions
Spaces_of_test_functions_and_distributions
Function reducing distance between all points
continuous and hence uniformly continuous (for a Lipschitz continuous function, the constant k is no longer necessarily less than 1). A contraction mapping has
Contraction_mapping
Real-valued function
\operatorname {BMO} } functions modulo the space of constant functions on the domain considered. As the name suggests, the mean or average of a function in BMO {\displaystyle
Bounded_mean_oscillation
Operation in mathematical calculus
− a) is the integral of the constant function with value M over [a, b]. In addition, if the inequality between functions is strict, then the inequality
Integral
Multiplicative function in number theory
^{2}n}{n}}=-2\gamma ,} where γ {\displaystyle \gamma } is Euler's constant. The Lambert series for the Möbius function is ∑ n = 1 ∞ μ ( n ) q n 1 − q n = q , {\displaystyle
Möbius_function
One-dimensional complex manifold
functions are constant, or on which all bounded harmonic functions are constant, or on which all positive harmonic functions are constant, etc. To avoid
Riemann_surface
Function space of all functions whose derivatives are rapidly decreasing
mathematics, Schwartz space S {\displaystyle {\mathcal {S}}} is the function space of all functions whose derivatives of all orders are rapidly decreasing. This
Schwartz_space
Smooth manifold with an inner product on each tangent space
}{4}}(x_{1}^{2}+\cdots +x_{n}^{2}))^{2}}}} has constant curvature κ. Any two Riemannian manifolds of the same constant curvature are locally isometric, and so it follows
Riemannian_manifold
Concept in statistics
closed form, but not the normalization constant. An example is the normal distribution. Its probability density function is p ( x | μ , σ 2 ) = 1 2 π σ 2 e
Kernel_(statistics)
Integral expressing the amount of overlap of one function as it is shifted over another
1983, Chapter 1). More generally, if either function (say f) is compactly supported and the other is locally integrable, then the convolution f∗g is well-defined
Convolution
Two theorems about families of holomorphic functions
that a family of holomorphic functions defined on an open subset of the complex numbers is normal if and only if it is locally uniformly bounded. A family
Montel's_theorem
Index of articles associated with the same name
Open mapping theorem (complex analysis), states that a non-constant holomorphic function on a connected open set in the complex plane is an open mapping
Open_mapping_theorem
Types of special mathematical functions
the reciprocal of Γ(z) is an entire function, the coefficients in the rightmost sum are well-defined, and locally the sum converges uniformly for all
Incomplete_gamma_function
Matrix of partial derivatives of a vector-valued function
amount of "stretching", "rotating" or "transforming" that the function imposes locally near that point. For example, if (x′, y′) = f(x, y) is used to
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
Function that "converges" to periodicity
Besicovitch, amongst others. There is also a notion of almost periodic functions on locally compact abelian groups, first studied by John von Neumann. Almost
Almost_periodic_function
Function with a multiplicative scaling behaviour
homogeneity. Every homogeneous real function is positively homogeneous. The converse is not true, but is locally true in the sense that (for integer degrees)
Homogeneous_function
the Kirillov model for π is a representation π on a space of locally constant functions f on F* with compact support in F such that π ( ( a b 0 1 ) )
Kirillov_model
connected (when p is large enough), or that the locally constant functions on these graphs are constant, so that the eigenspace for the first eigenvalue
Superstrong_approximation
Topological space that locally resembles Euclidean space
chart is defined, is locally constant), each connected component has a fixed dimension. Sheaf-theoretically, a manifold is a locally ringed space, whose
Manifold
Statistical technique
the two previous sections we assumed that the underlying Y(X) function is locally constant, therefore we were able to use the weighted average for the estimation
Kernel_smoother
Class of mathematical functions
z = 0 {\displaystyle z=0} . This yields an entire elliptic function that has to be constant by Liouville's theorem. The coefficients of the above differential
Weierstrass_elliptic_function
Analytic function in mathematics
_{k-1}}}>1+\delta \,} for all k, where δ > 0 is an arbitrary positive constant, then f(z) is a lacunary function that cannot be continued outside its circle of convergence
Lacunary_function
Class of representations
algebraic description through the action of the Hecke algebra of locally constant functions on G. Deep studies of admissible representations of p-adic reductive
Admissible_representation
Study of space and shapes locally given by a convergent power series
topics in geometric function theory: A conformal map is a function which preserves angles locally. In the most common case the function has a domain and
Geometric_function_theory
Integral transform useful in probability theory, physics, and engineering
Laplace transform of a function is often an analytic function, meaning that it can be expressed as a power series that converges locally, the coefficients
Laplace_transform
Method to solve constrained optimization problems
comparing the values of the original objective function at the points satisfying the necessary and locally sufficient conditions. The method of Lagrange
Lagrange_multiplier
Product of the principal curvatures of a surface
radius R has constant positive curvature R−2 and a flat plane has constant curvature 0, these two surfaces are not isometric, not even locally. Thus any
Gaussian_curvature
LOCALLY CONSTANT-FUNCTION
LOCALLY CONSTANT-FUNCTION
Female
Spanish
Spanish form of Latin Constantia, CONSTANZA means "steadfast."
Boy/Male
Australian, British, Danish, English, French, German, Italian, Latin, Swedish, Swiss
Steadfast; Constant
Boy/Male
Tamil
Constant
Girl/Female
Latin English
Firm of purpose. Constancy, from the Latin Constantia.
Boy/Male
English Latin
Steady; stable.
Girl/Female
British, English
Similar to Constance; Used by 16th and 17th Century Puritans
Girl/Female
Spanish Italian
Constant.
Girl/Female
Australian, French, German, Latin, Spanish
Constancy; Steadfastness
Girl/Female
American, Australian, British, Christian, Dutch, English, French, German, Latin, Portuguese, Shakespearean, Swedish
Constancy; Steadfastness
Boy/Male
Latin English
Constant.
Female
English
Variant spelling of English Lallie, LALLY means "to babble."
Female
English
English form of Latin Constantia, CONSTANCE means "steadfast."Â
Surname or Lastname
French and English
French and English : from a medieval personal name (Latin Constans, genitive Constantis, meaning ‘steadfast’, ‘faithful’, present participle of the verb constare ‘stand fast’, ‘be consistent’). This was borne by an 8th-century Irish martyr. This surname has also absorbed some cases of surnames based on Constantius, a derivative of Constans, borne by a 2nd-century martyr, bishop of Perugia. Compare Constantine.English : perhaps also a nickname from Old French constant ‘steadfast’, ‘faithful’.
Girl/Female
Latin American English French Shakespearean
Firm of purpose. Constancy, from the Latin Constantia.
Girl/Female
Australian, German, Latin, Spanish, Swedish
Constancy; Steadfastness
Surname or Lastname
English and French
English and French : from the medieval female personal name Constance, Latin Constantia, originally a feminine form of Constantius (see Constant), but later taken as the abstract noun constantia ‘steadfastness’.English and French : habitational name from Coutances in La Manche, France, which was named Constantia in Latin (see above) in honor of the Roman emperor Constantius Chlorus, who was responsible for fortifying the settlement in ad 305.
Male
Polish
Polish form of Latin Constans, KONSTANTY means "steadfast."
Boy/Male
Latin
Constant.
Female
Romanian
Romanian form of Latin Constantia, CONSTANTA means "steadfast."
Male
French
French and Romanian form of Latin Constantinus, CONSTANTIN means "steadfast."Â
LOCALLY CONSTANT-FUNCTION
LOCALLY CONSTANT-FUNCTION
Boy/Male
Tamil
Jai Kishan | ஜய கிஷந  , ஜய கிஷநÂ
Victory of Lord Krishna
Boy/Male
Indian
Family, Caste, Race
Boy/Male
Indian, Sikh
Invincible Warrior
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Interesting
Boy/Male
German American Welsh Irish English
Spear.
Girl/Female
Indian
Beautiful, Flower, Beloved (Name of mother of Jesus)
Girl/Female
Muslim/Islamic
Integrity and Virtuous
Girl/Female
Hindu
Goddess Lakshmi
Boy/Male
Bengali, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
Quiet; Gentle
Boy/Male
British, English
Powerful
LOCALLY CONSTANT-FUNCTION
LOCALLY CONSTANT-FUNCTION
LOCALLY CONSTANT-FUNCTION
LOCALLY CONSTANT-FUNCTION
LOCALLY CONSTANT-FUNCTION
a.
Vocally or musically concordant; agreeably consonant; symphonious.
n.
An expression of assent to a bill or motion; an affirmative vote; also, a member who votes "Content.".
a.
harmonizing together; accordant; as, consonant tones, consonant chords.
adv.
In a vocal manner; with voice; orally; with audible sound.
adv.
In words; verbally; as, to express desires vocally.
n.
A principle, practice, form of speech, or other thing of local use, or limited to a locality.
n.
Limitation to a county, district, or place; as, locality of trial.
n.
The state or quality of being constant or steadfast; freedom from change; stability; fixedness; immutability; as, the constancy of God in his nature and attributes.
a.
To improve the condition of, morally, physically, financially, socially, or otherwise.
adv.
As a layman; after the manner of a layman; as, to treat a matter laically.
adv.
With respect to place; in place; as, to be locally separated or distant.
adv.
Constant; continual.
adv.
With constancy; steadily; continually; perseveringly; without cessation; uniformly.
adv.
In moral qualities; in disposition and character; as, one who physically and morally endures hardships.
adv.
By, with, or in, the mouth; as, to receive the sacrament orally.
a.
Not constant; inconstant; fickle; changeable.
adv.
In a logical manner; as, to argue logically.
a.
Not constant; not stable or uniform; subject to change of character, appearance, opinion, inclination, or purpose, etc.; not firm; unsteady; fickle; changeable; variable; -- said of persons or things; as, inconstant in love or friendship.
a.
A day of the present or current month; as, the sixth instant; -- an elliptical expression equivalent to the sixth of the month instant, i. e., the current month. See Instant, a., 3.
n.
A superior wine, white and red, from Constantia, in Cape Colony.